The first paragraph on the 20 July Plot's Wikipedia article says that no details of the peace plans have emerged, and it cites three independent sources, so I doubt we're likely to come up with much on that front unless one of our /r/AskHistorians members is in the middle of writing their thesis on it. That said, I'll attempt some informed speculation.

Judging from the text of the order that was planned to be sent to German military units in the event of the operation's success in a 1943 draft of the plot- "...the government of the Reich has declared a state of military emergency...and at the same time has transferred the executive power, with the supreme command of the Wehrmacht, to [Reserve Army commander Friedrich Fromm]"- the short-term plan was a classic coup installing a co-conspirator as head of state and absolute dictator, eventually transitioning to a civilian government under Carl Friedrich Goerdeler. At least, that was the plan at one point in time.

(EDIT: I lost a fight with a run-on sentence. The above originally misread section III.i and lacked information about Goerdeler's intended role, such that I thought the idea was a decentralized, piecemeal surrender, with individual theater commanders negotiating terms independently. This is inaccurate.)

Again judging from the article, the conspirators do not appear to have been fully united in purpose, or to have maintained a consistent plan over time from the conspiratorial group's formation in 1942 to their final attempt on 20 July 1944.

In support of a lack of unified purpose:

The conspirators...managed to initiate Erwin Rommel, the famed "Desert Fox", into their ranks...Although Rommel felt he had to..."come to the rescue of Germany," he thought killing Hitler would make him a martyr. Like some others, he wanted Hitler arrested and hauled before a court-martial for his many crimes.

In support of a lack of plan consistency from beginning to end:

By mid-1943 the tide of war was turning decisively against Germany. The Army plotters and their civilian allies became convinced that Hitler should be assassinated, so that a government acceptable to the western Allies could be formed, and a separate peace negotiated in time to prevent a Soviet invasion of Germany.

...

[In summer 1944] when Stauffenberg sent Tresckow a message...asking whether there was any reason for trying to assassinate Hitler given that no political purpose would be served, Tresckow's response was: "The assassination must be attempted, [whatever the cost]...For the practical purpose no longer matters; what matters now is that the German resistance movement must take the plunge before the eyes of the world and of history. Compared to that, nothing else matters."

So from the looks of it, there wasn't a single, well-thought-out, widely-endorsed plan for dealing with the peace, just a bunch of different people who thought things would be better if Hitler were gone, each for their own inconstant reasons.

If there was any single man who could be said to be the mastermind behind the July 20 plot, it would have to be Henning von Treckow, and it would be possible to further speculate on what kind of government that he would have liked to see based on his background and the quotes that conclude the article- but I don't think that would be terribly relevant, because he doesn't appear to have been plotting to position himself as the head of state, merely overthrow Hitler.

This deals with German resistance to Hitler generally, not the 20 July conspirators specifically, but you may still find it helpful: essentially, it states that many of the resistance groups (military or otherwise) had unrealistic expectations/hopes that involved giving back more distant and recent conquests but keeping Poland and territory lost to France and Belgium in World War I. The Allies' declaration that they would accept nothing but unconditional surrender in the Casablanca Conference at the beginning of 1943 made any detailed peace plan something of a pipe dream. Since the 20 July conspiracy largely formed in 1943-1944, that was probably part of the reason that they didn't make more of an effort to have a consistent, agreed-upon peace plan.

As Toptomcat said they were a little all over the place. The coup was large enough that different people got involved for different reasons. The folks at the top of the plot, Van Stauffenberg among them, were hoping that after Hitler was assassinated the Allies would just stop and everything could go back to how it was in 1938. Sorry, oops, our bad, that guy was nuts, he's gone now.

They were hoping to hang onto at least some of their territorial gains, Poland for instance. They'd basically blame everything on Hitler with the idea being now that he's gone Germany is back in the hands of responsible leaders . You should check out a book called Resistance and Conformity in the Third Reich for more detail.

I'm not sure how the coup plotters would have treated the war in the East and Russia. Someone else may know more detail on that.

Re gaining peace with Germany's then enemies: Adam von Trott zu Solz was to be in charge of foreign relations. He tried to contact the British government among others but they ignored him. The concept of a peace offering by nationalistic minded people was foreign to them to put it mildly. Germany had to be defeated as a whole. There was never plan on how to deal with the Allies in case of a successful coup. In retrospect, it would have been irrelevant anyway because all the decisive battles had been lost already, which was the major motivating facor for the resistance in the German military who were no democrats by any stretch of imaginations (especially Stauffenberg himself).

Unfortunately, I don't have any English sources on this subject. In case any interested German is reading this: http://www.ifz-muenchen.de/heftarchiv/2004_3_2_daniel.pdf It deals with von Trott zu Solz's efforts to make conntact with British leadership.

A very good insight into what the German's wanted from the Allies is contained in the book "Bodyguard of Lies" by Anthony Cave Brown. Brown was in the OSS and this book is an in-depth look into the covert activity of the Allies and their contacts inside Germany. A very worthwhile read, it will answer the questions you are asking.